What does the monster symbolize?
The creature (much better word than monster) represents a range of ideas and concerns in the novel. Consider the following:
It may be a symbol of science - the novel repeatedly posits science as an alternative way of understanding the world to that offered by religion - the creature represents this in both its power and its deformities (both physical and moral) -
It may be a symbol of Viktor's and society's mysogyny - it is created without the natural loving process of a sexual relationship - the creature's initial creation keeps Frankenstein from being with Elizabeth, as does the murder on his wedding night - highly symbolic.
It may be a symbol of the parent child relationship: it grows up nameless unloved untutored and a moral lesson to parents about their obligations to their children. Recall Shelley's own tragedies losing mother and growing up most alone.
It may be a symbol of human nature, an argument against original sin: even untutored, the creature is initially good until maltreated by society around him, whereupon its rage took over. Notice however that the creature's rage is only directed at those connected to Frankenstein - or others who have hurt him - it is not a loose cannon!
It may be a symbol of the outcast from society: the weak the poor the dispossessed and a comment on the way that society treats them.
The creature is symbolic of the human being born as a blank slate, Voltaire's "tabula rasa," ready to receive input from the society in which it is born. The creature was "born good" but was turned to evil to rejection from society as a whole, but especially by his creator.
Voltaire's premise was significant in the field of education. He was explicit in stating that society has a responsibility for teaching the child to "be good." The creature also demonstrates that accountability for evil is in society, not in the individual, who he did not believe was born with the traditional notion of original sin. Sin is from the outside, never from within.
However, Shelley is ambiguous in this area. While the creature is a product of his rejecting environment, Victor turned "evil" despite a loving family and opportunities not granted to many people of his time. With age, Shelley backed away from the humanist notion of the tabula rasa, especially after her husband Percy's death.
I agree with all of the above, and I might add that in the human nature, we tend to judge too much. We judge others by the color of their skin, their weight, if they have acne or not, if they dress stylishly, etc. The creature is a loving creation who only wants to be loved and accepted. However, because of his appearance, he is rejected everywhere he goes, and sometimes rather violently. It is a sad commentary on our society.